Complex systems modeling approaches offer the means to examine the way in which local interactions between system components form emergent systems. Using these bottom‐up modeling approaches in combination with geographic information systems (GIS) and geospatial data, the complexity inherent to spatial phenomena including geographical, urban, ecological, or geophysical systems can be captured and represented. Scientific research in the field of network science also uses a complex systems approach to conceptualize, model, and analyze geospatial systems as networks. Despite having common characteristics, complexity, geographic information, and network sciences are not yet fully integrated. Therefore, the main objective of this article is to provide a comprehensive review of scientific research related to network theory and to evaluate the potential of their integration with complex systems modeling approaches originating in the field of geographic information science (GISc). This article finds that existing literature focuses on characterizing static spatial network structures to better understand the dynamics that take place on or within them. This article argues for a necessity in research advancements to explore the way in which real spatial network structures evolve in response to spatial dynamics and advocates for the integration of geographic automata systems (GAS) modeling approaches with networks to do so. The mathematical foundation for graph theory, including the measures that are used to describe networks and the theoretical graph types, are introduced. Geospatial applications of networks and graph theory are also presented. Examples of network‐based automata models are presented as avenues for future research work in evolving spatial networks as part of GISc and computational geography.

中文翻译：

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复杂的空间网络：理论和地理空间应用

复杂的系统建模方法提供了检查系统组件之间的局部交互形成紧急系统的方式的方法。通过将这些自下而上的建模方法与地理信息系统（GIS）和地理空间数据结合使用，可以捕获和表示空间现象所固有的复杂性，包括地理，城市，生态或地球物理系统。网络科学领域的科学研究还使用复杂的系统方法来将地理空间系统概念化，建模和分析为网络。尽管具有共同的特征，但是复杂性，地理信息和网络科学尚未完全集成。因此，本文的主要目的是提供有关网络理论的科学研究的全面综述，并评估其与起源于地理信息科学（GISc）的复杂系统建模方法集成的潜力。本文发现现有文献集中于表征静态空间网络结构，以更好地了解在其上或内部发生的动力学。本文认为有必要在研究方面进行探索，以探索实际的空间网络结构如何响应空间动力学而演化，并主张将地理自动机系统（GAS）建模方法与网络集成。图论的数学基础 介绍了用于描述网络的度量和理论图类型。还介绍了网络和图论的地理空间应用。提出了基于网络的自动机模型的示例，作为在GISc和计算地理学中不断发展的空间网络中未来研究工作的途径。